We introduce a new set-open topology on function spaces namely the semi-compact-open topology. The topology of uniform convergence on semi-compacta lies between the topology of pointwise convergence and the topology of uniform convergence. We show that for the space of quasicontinuous functions the topology of uniform convergence on semi-compacta coincides with the semi-compact-open topology. We also investigate results relating to induced functions, cardinal invariants and Ascoli like properties on the space of quasicontinuous functions when equipped with the topology of uniform convergence on semi-compacta.
Barman et al. (Mon,) studied this question.